You need to use BVH to create a skeleton in the rest position, then you move the skeleton GameObject to align with the rest position of the model, then you use MeshSkinner to apply the skeleton to the model. The problem here is that the BVH rest position has the arms straight down but the model rest position is in T-pose.
In the example below I rearranged the arms of the model you linked to so they became a child of the shoulder GameObject and then I rotated and repositioned the shoulders so the model was no longer in T-pose. This was done in Unity with "dummy_obj.obj" (didn't use Blender or something else). Now the rest pose of the BVH was roughly the same as the rest pose of the model and I could align the skeleton with the model.
The arrangements was made in Unity's play mode with a debug BVH skeleton (xray turned on). After everything looked good I copied the root "dummy_obj" and stopped play mode. The model was reset, I deleted it and then pasted the arranged version. Now when I enter play mode the model is aligned with the skeleton created by BVH.
Finally I call BVH's static animateSkeleton() helper method to animate the thing. I used "Full-body Walking" from the page you linked to (notch-format.bvh), it was tiny so I scaled it up by 100 to fit the model. I imported the BVH at 10 fps and looping between frame -36 and -10 with an extra loop keyframe added produced a seamless walking animation. However, due to the rest pose of the BVH the MeshSkinner incorrectly thinks part of the model's hip is part of the hand bone. It might be possible to tweak this issue away in MeshSkinner before the work call, but best would be to find .bvh files that have the skeleton rest positions in T-pose or A-pose.
BVH bvh = new BVH("C:/temp/notch-format.bvh", -10);
bvh.scale(100);
GameObject skeleton = bvh.makeDebugSkeleton(animate:false, xray:true);
MeshSkinner ms = new MeshSkinner(GameObject.Find("dummy_obj"), skeleton);
ms.workAndFinish();
Animation a = BVH.animateSkeleton(skeleton, bvh.makeAnimationClip(-36, -10, true));